Escape problem for irreversible systems

Robert S. Maier, D. L. Stein

    Research output: Contribution to journalArticle

    Abstract

    The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotic behavior of fundamental quantities such as the mean escape time. In this paper we present a general technique for analyzing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the possibility of focusing along the escape path.

    Original languageEnglish (US)
    Pages (from-to)931-938
    Number of pages8
    JournalPhysical Review E
    Volume48
    Issue number2
    DOIs
    StatePublished - 1993

    Fingerprint

    escape
    Detailed Balance
    Asymptotic Behavior
    Path
    Metastable States
    Nonlinear Dynamical Systems
    Systems Engineering
    Probable
    Chemistry
    Biology
    Continuous Time
    Resolve
    Simplify
    Ordinary differential equation
    Partial differential equation
    Physics
    biology
    Computing
    systems engineering
    metastable state

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Condensed Matter Physics
    • Statistical and Nonlinear Physics

    Cite this

    Escape problem for irreversible systems. / Maier, Robert S.; Stein, D. L.

    In: Physical Review E, Vol. 48, No. 2, 1993, p. 931-938.

    Research output: Contribution to journalArticle

    Maier, Robert S. ; Stein, D. L. / Escape problem for irreversible systems. In: Physical Review E. 1993 ; Vol. 48, No. 2. pp. 931-938.
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